The Daily Star says the Italian giants are in the hunt to sign the Liverpool full-back on a free transfer next summer.
Johnson's current £110,000 a week Liverpool deal expires at the end of this season.
And Roma have made contact with Johnson's representatives to register their interest.
Johnson can sign a pre-contract agreement with a foreign club from January 1 ahead of a summer switch.
Last season's Italian league runners-up are determined to be at the front of the queue.
A free transfer to Roma is likely to land Johnson a pay rise and also offer him the chance to revive his career.
Johnson is represented by the Stellar Group, the same firm who look after ex-England star Cole and negotiated his move to Roma.
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